The easiest way would be use a linear regression model.

One of the most popular softwares to conduct GWAS is by far PLINK: https://www.cog-genomics.org/plink2

Before doing the GWAS, however, you should do various QC steps. I recommend you to read this tutorial by D. Balding: http://www.nature.com/nrg/journal/v7/n10/abs/nrg1916.htmlalthough - the discussion is mainly concerned on human GWAS though.

I would think that conducting a GWAS in canines might pose different difficulties as well. For instance, is there population structure in your sample? Can this be capture by a PCA? if so you might one to add the first PCs as covariates in your linear regression. However, if there is other type of populations structure in your sample such as cryptic relatedness or other kind of familial structure, you might want to consider another approach such as mixed linear model (MLM) . There are many softwares available too, to conduct GWAS using MLM. Just try googling "mixed linear models GWAS" and you will find a bunch.

HTH